Industry: Energy
Product: ModelRisk
Application: Probabilistic N-1 / N-2 contingency analysis for an ISO control area

Holding the Lights On at 92% Renewable Penetration: Probabilistic N-1 Analysis with ModelRisk

The NERC reliability standard is famously phrased as a deterministic guarantee: the system must remain stable after any single credible contingency (N-1) and most double-contingencies (N-2). The metric the regulator actually tracks, however, is Loss of Load Expectation (LOLE) — an inherently probabilistic quantity, capped at 0.1 days/year for most reliability councils (the "one-day-in-ten-years" standard). For a 14 GW peak summer control area pushing 92% instantaneous renewable penetration on the right day in May, deterministic N-1 says everything is fine. The LOLE calculation, done properly, says 0.27 days/year — nearly 3x the standard — driven entirely by the joint distribution of load, wind, solar and forced-outage events.

The annual loss-of-load distribution below makes the gap visible: most simulated years see no shortfall at all, but a heavy tail of multi-day high-load / low-wind clusters drags the mean LOLE to 0.27 days/year, well past the 0.1-day NERC standard a deterministic study never sees.

What "joint distribution" actually means here

The deterministic N-1 calculation takes peak load, derates renewables to their winter-capacity-factor floor, and assumes the largest single unit is offline. Three independent worst-case assumptions, ANDed together, look conservative. They aren't — they miss the days when load is moderate, wind is below P10, and two mid-sized units have a forced outage at the same time.

• Hourly load modelled as Normal( μ(t), σ ) with μ driven by an ambient-temperature day-type table fitted to 8 years of ISO data; σ = 2.1% of mean for day-ahead, widening to 6.4% over week-ahead horizons. Total annual peak modelled with a Gumbel distribution fitted to the annual-maximum series — Gumbel is the natural extreme-value form here and beats a Normal fit on the upper tail.
• Wind output per hour as Beta scaled to installed capacity, with Beta parameters that themselves depend on synoptic regime (a 3-state Markov chain over high-pressure / frontal / convective patterns).
• Solar output as scaled clear-sky × Beta(cloud transmittance), with a deterministic eclipse/seasonal envelope.
• Generator forced outages as independent Bernoulli draws per unit per hour, with rates from the NERC GADS database (combined-cycle ≈ 6%, simple-cycle ≈ 11%, nuclear ≈ 2%, coal ≈ 9% EFOR), aggregated as a mixture of binomials across the fleet.
• Wind–load correlation is the term most often forgotten: ρ = -0.22 in summer, the worst sign because wind drops just when load is highest. Modelled with a Gaussian copula on the residuals.

LOLE and EUE: what the deterministic view missed

8,760 hours × 50,000 simulated years gives 438 million hour-scenarios. For each, available capacity (generation − forced outages − reserves committed) is compared to demand. A loss-of-load event is any hour where available < demand. EUE (Expected Unserved Energy) accumulates the MWh shortfall.

The deterministic study reported a single-number LOLE of 0.04 days/year by handling each stress in isolation. The Monte Carlo result of 0.27 days/year, with EUE of 412 MWh/year, reflects the joint behaviour. The 99th percentile of annual lost-load hours is 96 hours, dominated by 3–5 day high-load / low-wind clusters in late August. Meeting the 0.1 days/year standard demands either ~520 MW additional firm capacity, ~1.2 GWh of additional storage, or a combination — and the trade-off between those two is what the next section answers.

What actually drives the EUE

The wind capacity factor in summer peak weeks is the biggest single driver — a 5-percentage-point downward shift moves EUE by 180 MWh/year. Combined-cycle EFOR is second; this is the input that the ISO's reliability committee had been sourcing from a single multi-year average rather than from the GADS distribution. Replacing the point estimate with the distribution moved 28 MWh/year into EUE that had been invisible.

Mitigation options compared on the same yardstick

The team evaluated three contingency-response paths against the same simulation:

A 350 MW battery cuts EUE the most per dollar in the body of the distribution but does little in the extreme-cluster tail (the battery is depleted by hour 12 of a 4-day event). A 220 MW peaker cuts the tail cleanly but pays a heavier fixed cost. A demand-response program of 180 MW — economically the cheapest — cuts the body well but has high uncertainty in delivered MW (the DR-yield distribution is Beta(3, 1.5) on declared capacity, with realised yield well below 100% on the days that matter). The portfolio answer, chosen by the planning committee, is 200 MW battery + 120 MW peaker + 90 MW DR — keeping EUE inside the standard at 60% of the single-asset cost.

What changed

• LOLE reported with confidence bands rather than a point — the regulatory filing now shows 0.27 (median) with a 90% CI [0.18, 0.41] days/year, allowing the commission to see the joint uncertainty rather than a single deterministic figure.
• Mitigation portfolio replaced single-asset answer — the 200 MW battery + 120 MW peaker + 90 MW DR composite achieves the 0.1 day/year standard at $61M less capital than the original "build one 520 MW peaker" plan.
• Forced-outage inputs upgraded from point averages to distributions sourced from GADS, exposing 28 MWh/year of EUE that the point-average had hidden.
• Wind–load anti-correlation explicitly modelled (ρ = -0.22 in summer); previous deterministic studies effectively assumed ρ = 0, which under-stated joint stress events.

ModelRisk Functionality Used

• Mixture of binomials for fleet-wide forced outage, parameterised per technology from the NERC GADS database — replaces single-point EFOR averages.
• 3-state Markov regime model for wind synoptic conditions, driving the Beta parameters that shape hourly capacity factor.
• Gumbel fit to annual-maximum load, validated against 8 years of ISO peak data — Normal fit failed the Anderson–Darling test on the upper tail.
• Gaussian copula on wind–load residuals (ρ = -0.22) — propagates the anti-correlation that drives high-stress hours.
• EUE accumulation across 438M hour-scenarios, post-processed into LOLE, EUE and 99th-percentile hour-cluster duration for the regulatory filing.
• Mitigation-portfolio scoring that compared three single-asset options and one composite on the same EUE-distribution yardstick, selecting the composite on $/MWh-cleared basis.

Reliability is not "we passed N-1." Reliability is a number with a unit (days/year) and a confidence interval. Monte Carlo simulation in ModelRisk is what turns the latter into an auditable quantity the planning committee and the regulator can both defend.